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Global asymptotic stability of 3-species mutualism models with diffusion and delay effects. (English) Zbl 1179.35332

Summary: In this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition. Our approach to the problem is based on inequality skill and the method of the upper and lower solutions for a more general reaction-diffusion system. Finally, some numerical simulations are given to illustrate our results.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A15 Variational methods applied to PDEs
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References:

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